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Impedance-Based Sensitivity Analysis for Stability Enhancement of LCC-HVDC Links Connected to Weak Grids Using Grid-Forming Converters

Luis A. Garcia-Reyes, Anup Joshi, Javier Renedo, Macarena Martin-Almenta, Oriol Gomis-Bellmunt, Eduardo Prieto-Araujo, Vinicius A. Lacerda, Xavier Guillaud

arXiv:2609.10774v1eess.SYcs.SY

TL;DR

Assessing LCC-HVDC stability in weak grids is challenging when converter models are black boxes and commutation complicates impedance identification. The paper combines frequency-domain identification, GNC, and modal impedance analysis; its sensitivity study reports that GFM-VSC integration shifts the stability limit to a lower SCR.

  • Problem

    Weak-grid LCC-HVDC stability analysis is challenged by unavailable internal converter models and commutation-related nonlinearities and frequency coupling that complicate identification.

    Source: §I · p. 1

  • Method

    The paper identifies LCC-HVDC and grid impedances in the frequency domain, applies GNC for multivariable stability assessment, and uses modal impedance decomposition with participation factors.

    Source: §I · p. 2

  • Results

    SCR 1.94 is the reported GFM-VSC-supported stability limit, shifted from the standalone link's approximately 3.09 limit.

    Source: §IV · p. 6

  • Takeaways & Limitations

    The impedance-based approach reproduces system dynamics without detailed models and supports stability assessment and enhancement under weak-grid conditions.

    Source: §IV · p. 6

Abstract

from arXiv · show

This paper presents a frequency-domain, impedance-based sensitivity methodology for stability assessment and enhancement of line-commutated converter HVDC (LCC-HVDC) links operating under weak-grid conditions. The methodology integrates frequency-domain identification tailored for black-box systems, the Generalized Nyquist Criterion (GNC) for multivariable stability assessment, and modal impedance decomposition with participation-factor analysis to locate and interpret interaction mechanisms. The approach is validated against a detailed linearized state-space model and nonlinear EMT simulations of an LCC-HVDC benchmark. A sensitivity study varying the grid short-circuit ratio (SCR) reveals a stability limit for the standalone LCC-HVDC link and demonstrates that the integration of a grid-forming voltage source converter (GFM-VSC) substantially increases the stability margin.

I. INTRODUCTION

The paper addresses challenges in assessing LCC-HVDC stability in weak grids when converter models are unavailable and commutation complicates frequency-domain identification. It introduces an impedance-based sensitivity methodology and uses it to assess stability limits and the effect of grid-forming support.

I. INTRODUCTION

  • Renewable penetration can reduce grid strength and short-circuit capability, increasing LCC-HVDC susceptibility to commutation failures during disturbances.LCCs cannot supply reactive power during disturbances, and VSC-based support may introduce additional sub- and super-synchronous interaction challenges in weak grids.Source: §I · p. 1
  • Black-box LCC-HVDC analysis is complicated by commutation nonlinearities and frequency coupling, while reliable EMT identification validation without detailed state-space models remains challenging.Manufacturer IP restrictions can prevent access to internal converter models, limiting detailed state-space analysis in multi-vendor settings.Source: §I · p. 1
  • The proposed methodology combines frequency-domain impedance identification, GNC, and modal impedance decomposition with participation factors for weak-grid LCC-HVDC sensitivity analysis.The impedance models are validated against linearized state-space and nonlinear EMT models, and an SCR study assesses the standalone link and a GFM-VSC-supported system.Source: §I · pp. 1–2

II. IMPEDANCE-BASED METHODOLOGY ANALYSIS

The methodology represents the system as interacting subsystems, uses frequency-domain impedance identification and the Generalized Nyquist Criterion for stability assessment, and applies modal decomposition and participation factors to interpret oscillations.

II. IMPEDANCE-BASED METHODOLOGY ANALYSIS

  • The system is divided at the PCC into Norton and Thévenin subsystem equivalents, whose closed-loop response relates subsystem currents, voltage, admittance, and impedance.The closed-loop denominator becoming undefined indicates instability.Source: §II · p. 2
  • For MIMO stability assessment, the GNC evaluates eigenvalue loci of the minor-loop gain; stability is ensured when none encircle the critical point (−1, j0).The eigenvalues are those of L(s).Source: §II · p. 2
  • Frequency-domain scanning obtains subsystem admittance and impedance, with this work using the dq frame to simplify analysis while capturing small-signal phenomena.The text identifies scanning as a practical approach when model complexity and IP restrictions limit access to detailed models.Source: §II · p. 2
  • Modal decomposition expresses the system admittance through eigenvector and eigenvalue matrices, while participation factors identify each input's contribution to a mode.The right and left eigenvector matrices and diagonal eigenvalue matrix define the decomposition; its diagonal terms are modal impedances.Source: §II · p. 2

III. IMPEDANCE-BASED SENSITIVITY ANALYSIS

The analysis uses a simplified averaged LCC-HVDC model connected to a grid equivalent, then examines weak-grid stability with and without a GFM-VSC.

III. IMPEDANCE-BASED SENSITIVITY ANALYSIS

  • The benchmark adopts a simplified averaged LCC-HVDC link, modeled as a controlled current source with ideal DC voltage control, connected to a grid equivalent.The paper states that this reduced model reproduces the dynamics of the detailed switching model.Source: §III · p. 2, Figure 2 · p. 3
  • For stability enhancement, a GFM-VSC connects at the PCC through a 30-km overhead line and uses current control with VSM-based synchronization and a PLL.The GFM-VSC control and system parameters are listed separately in Tables III and IV.Source: §III · p. 3
  • The analysis proceeds from model validation to standalone LCC-HVDC stability limits under weak-grid conditions, then to stability enhancement with a GFM-VSC.The system and LCC-HVDC control parameters are listed in Tables I and II.Source: §III · p. 3, Table I · p. 3, Table II · p. 3

A. Impedance-Based Model Validation

The identified impedance model agrees with linearized and nonlinear EMT responses; GNC and modal analyses confirm stability while locating weakly damped oscillations.

A. Impedance-Based Model Validation

  • The identified impedances use a 5% nominal-voltage series perturbation, with 114 logarithmically spaced frequency points across 1–1000 Hz.The study evaluates the operating point P = 1 pu.Source: A. Impedance-Based Model Validation · p. 3
  • At SCR 10 (Zg = 0.1 pu), identified dq admittance agrees with the linearized response, and linearized and EMT models agree after a 0.1 pu DC-current step.The comparisons are shown in the dq frequency response and time-domain validation figures.Source: Figure 5 · p. 4, Figure 6 · p. 4, A. Impedance-Based Model Validation · p. 4
  • No eigenvalue locus encircles the GNC critical point, confirming stability consistently with state-space analysis; the closed-loop modes nevertheless include two oscillatory modes with damping below 5%.The minimum distances of λ1 and λ2 to the critical point occur at 153 Hz and 253 Hz, respectively.Source: Figure 7 · p. 4, A. Impedance-Based Model Validation · p. 4, Table V · p. 4
  • Modal impedance peaks confirm the system oscillatory modes, and no negative modal impedances occur within the analyzed frequency range.Participation factors associate the first mode predominantly with the grid and the second with the LCC-HVDC link.Source: Figure 8 · p. 4, A. Impedance-Based Model Validation · p. 4

B. Stability limit of the LCC-HVDC system

The standalone LCC-HVDC link reaches its weak-grid stability limit at SCR 3.09. Modal analysis identifies grid- and LCC-dominated interactions and a strong grid-dominated instability below the limit.

B. Stability limit of the LCC-HVDC system

C. Stability Enhancement Using a GFM-VSC

Adding a GFM-VSC substantially lowers the SCR stability limit for the LCC-HVDC system. Modal results identify weakly damped behavior at the limit and strong instability below it.

C. Stability Enhancement Using a GFM-VSC

IV. CONCLUSIONS

The paper concludes that impedance-based sensitivity analysis assesses LCC-HVDC stability in weak grids, including when detailed models are unavailable. It reports that GFM-VSC integration shifts the stability limit from SCR 3.09 to 1.94.

IV. CONCLUSIONS

  • The SSA impedance-based approach reproduces system dynamics and is presented as a model-agnostic method for stability assessment when detailed models are unavailable.Source: §IV · p. 6
  • The standalone LCC-HVDC link has a stability limit near SCR 3.09, dominated by a low-frequency, grid-dominated oscillatory mode.Source: §IV · p. 6
  • Integrating a GFM-VSC shifts the stability limit to SCR 1.94 and favorably reshapes the system's modal distribution.The paper identifies GFM-VSCs as potential dynamic support devices in weak grids.Source: §IV · p. 6
  • Future work will examine more demanding dynamic scenarios, advanced GFM controls, and coordinated operation of multiple support devices in highly weakened grids.Source: §IV · p. 6
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